The user is unable to view "Close" option for Sub-task, though he have all permissions and there is no any condition in workflow. Also no issue with intergrity checker.
Those conditions are almost certainly the problem. Having them all as "and" might be a bit too strict, but as Renjith says, you need to debug them - either check that all three are met (because they're all ANDs) or remove them from the workflow and see if the user can then proceed.
If there are no conditions in the workflow, then the close transition should be there.
Can you tell us what version of Jira you are on, and give us a screenshot of what actions the user sees across the entire workflow-actions bar, and what your workflow is (use workflow view if available). Or, if screenshots don't work, just track across the workflow menu-bar and note down what is offered, including all options in the drop-down,
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